Question: Solve for $x$ and $y$ using elimination. ${-5x-y = -46}$ ${-2x+y = -17}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-7x = -63$ $\dfrac{-7x}{{-7}} = \dfrac{-63}{{-7}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-5x-y = -46}\thinspace$ to find $y$ ${-5}{(9)}{ - y = -46}$ $-45-y = -46$ $-45{+45} - y = -46{+45}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 9}$ into $\thinspace {-2x+y = -17}\thinspace$ and get the same answer for $y$ : ${-2}{(9)}{ + y = -17}$ ${y = 1}$